Carbon nanotubes (CNTs), the one-dimensional allotropes of carbon, have attracted noteworthy research interest since their discovery in 1991 owing to their large aspect ratio, low mass density, and unique chemical, physical, and electronic properties that provide exciting possibilities for nanoscale applications. Nonetheless, two major issues should be considered when working with this sort of nanomaterial: their strong agglomerating tendency, since they are typically present as bundles or ropes of nanotubes, and the metallic impurities and carbonaceous fragments that go along with the CNTs. The successful utilization of CNTs in a wide variety of applications—in particular, in the field of polymer composites—depends on their uniform dispersion and the development of a strong chemical interaction with the polymeric matrix. To achieve these aims, chemical functionalization of their sidewalls and tips is required. In this article, a brief overview of the different approaches for CNT modification using polymers is provided, focusing on the covalent functionalization via “grafting to” or “grafting from” strategies. The characteristics and advantages of each approach are thoroughly discussed, including a few typical and recent examples. Moreover, applications of polymer-grafted CNTs as biosensors, membranes, energy storage substances, and EMI shielding are briefly described. Finally, future viewpoints in this vibrant research area are proposed.